........................................................................... Below are two lists of the largest orders of a group of automorphisms of a compact Riemann surface of given genus g, for g between 2 and 301. The first list is for the orientation-preserving case, and the second is for the case where orientation-reversing automropshims are allowed. In each case the type(s) are given for the Fuchsian or NEC groups from which the corresponding actions can be obtained. Here the types (p,q,r) and (p,q,r,s) denote the orientation-preserving signatures (0; +; [p,q,r]; {-}) and (0; +; [p,q,r,s]; {-}), which may be called "triangular" and "quadrangular", respectively. Similarly, the types (p,q,r)* and (p,q,r,s)* denote the NEC-group signatures (0; +; [-]; {(p,q,r)}) and (0; +; [-]; {(p,q,r,s)}), respectively, with orientation-reversing subgroup of index 2. ********************************************************************** * Note: corrections were made in February 2015 to four cases in the * * second list, because the original version of the second list did * * not take into account the possibility of non-standard reflections. * * The corrections were made for the following genera: * * Genus 101 - Largest order increased from 3200 to 4800 * * Genus 170 - Largest order increased from 4056 to 8112 * * Genus 281 - Additional signature included for largest order * * Genus 290 - Additional signature included for largest order * ********************************************************************** Marston Conder September 2012 ........................................................................... Some observations can be made in the orientation-preserving case: (a) An upper bound for these largest orders is 84(g-1), occurring for type (2,3,7), but this bound is attained for very few genera, namely g = 3, 7, 14, 17, 118, 129 and 146 only (b) A lower bound for these largest orders is 8(g+1), occurring for type (2,4,2(g+1)), and this bound is attained for few more genera, namely g = 23, 47, 88, 95, 116, 119, 142, 143, 160, 167, 178, 188, 208, 214, 215, 236, 250, 263, 268 and 296 (c) The order 8(g+3) occurs for type (2,4,g+3) quite frequently, namely for g = 12, 18, 24, 30, 48, 54, 60, 84, 90, 93, 108, 114, 138, 150, 162, 168, 174, 180, 186, 189, 198, 204, 222, 228, 234, 237, 240, 258, 264, 270, 288, 294 (d) The cases (b) and (c) above account for 52 values of g -- that is, about one-sixth of all genera in the given range (e) The "next best" after (2,3,7) are (2,3,8), (2,4,5), (2,3,9), (2,3,10), (2,3,11), giving orders 48(g-1), 40(g-1), 36(g-1), 30(g-1) and (132/5)(g-1), occurring for 28, 10, 6, 14 and 1 values of g, respectively (f) From (a) and (e) we see that the order exceeds 24(g-1) for 66 values of g (g) The maximum order is 24(g-1) when the optimum type is (2,3,12) or (2,4,6) or (3,3,4), and this happens for 72 values of g (h) From (f) and (g) we see that the order is 24(g-1) or more for 138 values of g, which is almost half of the given range (i) The order 16(g-1) is exceeded for 148 values of g, which is just under half of the given range (j) The order 16(g-1) is achieved or exceeded for 171 values of g, which is well over half of the given range (k) If M_g denotes the maximum group order, then the average value of the ratio M_g/(g-1) across the given range is approx. 21.99. Also some further observations can be made from the data that lies behind this list: (l) The most frequent types that occur among all "large" group actions on surfaces with genus g in the given range are as follows: Type (2,6,6) ... 127 genera Type (2,3,12) ... 96 genera Type (2,8,8) ... 94 genera Type (2,12,12) ... 94 genera Type (2,4,12) ... 91 genera Type (2,4,8) ... 80 genera Type (2,6,12) ... 64 genera Type (2,2,2,3) ... 63 genera Type (2,4,6) ... 55 genera Type (2,5,10) ... 41 genera Type (2,4,20) ... 41 genera Type (2,20,20) ... 41 genera (m) None of these cases appears to exhibit a replicable arithmetic progression of genera. [There should be a good reason for that.] ........................................................................... Case A: Orientation-preserving automorphisms Genus 2 Maximum order 48 occurring for type(s) { (2,3,8) } Genus 3 Maximum order 168 occurring for type(s) { (2,3,7) } Genus 4 Maximum order 120 occurring for type(s) { (2,4,5) } Genus 5 Maximum order 192 occurring for type(s) { (2,3,8) } Genus 6 Maximum order 150 occurring for type(s) { (2,3,10) } Genus 7 Maximum order 504 occurring for type(s) { (2,3,7) } Genus 8 Maximum order 336 occurring for type(s) { (2,3,8) } Genus 9 Maximum order 320 occurring for type(s) { (2,4,5) } Genus 10 Maximum order 432 occurring for type(s) { (2,3,8) } Genus 11 Maximum order 240 occurring for type(s) { (2,4,6) } Genus 12 Maximum order 120 occurring for type(s) { (2,4,15) } Genus 13 Maximum order 360 occurring for type(s) { (2,3,10) } Genus 14 Maximum order 1092 occurring for type(s) { (2,3,7) } Genus 15 Maximum order 504 occurring for type(s) { (2,3,9) } Genus 16 Maximum order 720 occurring for type(s) { (2,3,8) } Genus 17 Maximum order 1344 occurring for type(s) { (2,3,7) } Genus 18 Maximum order 168 occurring for type(s) { (2,4,21) } Genus 19 Maximum order 720 occurring for type(s) { (2,4,5) } Genus 20 Maximum order 228 occurring for type(s) { (2,6,6) } Genus 21 Maximum order 480 occurring for type(s) { (2,4,6) } Genus 22 Maximum order 1008 occurring for type(s) { (2,3,8) } Genus 23 Maximum order 192 occurring for type(s) { (2,4,48) } Genus 24 Maximum order 216 occurring for type(s) { (2,4,27) } Genus 25 Maximum order 720 occurring for type(s) { (2,3,10) } Genus 26 Maximum order 750 occurring for type(s) { (2,3,10) } Genus 27 Maximum order 624 occurring for type(s) { (2,3,12) } Genus 28 Maximum order 1296 occurring for type(s) { (2,3,8) } Genus 29 Maximum order 672 occurring for type(s) { (2,4,6) } Genus 30 Maximum order 264 occurring for type(s) { (2,4,33) } Genus 31 Maximum order 720 occurring for type(s) { (2,4,6) } Genus 32 Maximum order 372 occurring for type(s) { (2,6,6) } Genus 33 Maximum order 1536 occurring for type(s) { (2,3,8) } Genus 34 Maximum order 1320 occurring for type(s) { (2,4,5) } Genus 35 Maximum order 544 occurring for type(s) { (2,4,8) } Genus 36 Maximum order 672 occurring for type(s) { (2,3,16) } Genus 37 Maximum order 1728 occurring for type(s) { (2,3,8) } Genus 38 Maximum order 444 occurring for type(s) { (2,6,6) } Genus 39 Maximum order 912 occurring for type(s) { (2,3,12) } Genus 40 Maximum order 936 occurring for type(s) { (2,3,12) } Genus 41 Maximum order 960 occurring for type(s) { (2,4,6) } Genus 42 Maximum order 410 occurring for type(s) { (2,5,10) } Genus 43 Maximum order 1512 occurring for type(s) { (2,3,9) } Genus 44 Maximum order 516 occurring for type(s) { (2,6,6) } Genus 45 Maximum order 1320 occurring for type(s) { (2,3,10) } Genus 46 Maximum order 2160 occurring for type(s) { (2,3,8) } Genus 47 Maximum order 384 occurring for type(s) { (2,4,96) } Genus 48 Maximum order 408 occurring for type(s) { (2,4,51) } Genus 49 Maximum order 1920 occurring for type(s) { (2,4,5) } Genus 50 Maximum order 1176 occurring for type(s) { (3,3,4), (2,4,6) } Genus 51 Maximum order 1200 occurring for type(s) { (2,3,12) } Genus 52 Maximum order 2448 occurring for type(s) { (2,3,8) } Genus 53 Maximum order 832 occurring for type(s) { (2,4,8) } Genus 54 Maximum order 456 occurring for type(s) { (2,4,57) } Genus 55 Maximum order 1296 occurring for type(s) { (2,3,12), (2,4,6) } Genus 56 Maximum order 1320 occurring for type(s) { (2,3,12), (2,4,6) } Genus 57 Maximum order 1344 occurring for type(s) { (2,3,12), (2,4,6) } Genus 58 Maximum order 1368 occurring for type(s) { (2,3,12) } Genus 59 Maximum order 928 occurring for type(s) { (2,4,8) } Genus 60 Maximum order 504 occurring for type(s) { (2,4,63) } Genus 61 Maximum order 1440 occurring for type(s) { (2,4,6) } Genus 62 Maximum order 732 occurring for type(s) { (2,6,6) } Genus 63 Maximum order 1488 occurring for type(s) { (2,3,12) } Genus 64 Maximum order 1512 occurring for type(s) { (2,3,12) } Genus 65 Maximum order 3072 occurring for type(s) { (2,3,8) } Genus 66 Maximum order 1014 occurring for type(s) { (2,3,26) } Genus 67 Maximum order 576 occurring for type(s) { (2,4,48) } Genus 68 Maximum order 804 occurring for type(s) { (2,6,6) } Genus 69 Maximum order 2448 occurring for type(s) { (2,3,9) } Genus 70 Maximum order 660 occurring for type(s) { (2,5,11) } Genus 71 Maximum order 672 occurring for type(s) { (2,6,8) } Genus 72 Maximum order 710 occurring for type(s) { (2,5,10) } Genus 73 Maximum order 2160 occurring for type(s) { (2,3,10) } Genus 74 Maximum order 876 occurring for type(s) { (2,6,6) } Genus 75 Maximum order 1776 occurring for type(s) { (2,3,12) } Genus 76 Maximum order 1800 occurring for type(s) { (2,3,12) } Genus 77 Maximum order 912 occurring for type(s) { (2,6,6) } Genus 78 Maximum order 1176 occurring for type(s) { (2,3,28) } Genus 79 Maximum order 1872 occurring for type(s) { (2,3,12) } Genus 80 Maximum order 948 occurring for type(s) { (2,6,6) } Genus 81 Maximum order 1536 occurring for type(s) { (2,3,16) } Genus 82 Maximum order 3888 occurring for type(s) { (2,3,8) } Genus 83 Maximum order 1312 occurring for type(s) { (2,4,8) } Genus 84 Maximum order 696 occurring for type(s) { (2,4,87) } Genus 85 Maximum order 4032 occurring for type(s) { (2,3,8) } Genus 86 Maximum order 1200 occurring for type(s) { (2,3,40) } Genus 87 Maximum order 2064 occurring for type(s) { (2,3,12) } Genus 88 Maximum order 712 occurring for type(s) { (2,4,178) } Genus 89 Maximum order 2640 occurring for type(s) { (2,3,10) } Genus 90 Maximum order 744 occurring for type(s) { (2,4,93) } Genus 91 Maximum order 3600 occurring for type(s) { (2,4,5) } Genus 92 Maximum order 2184 occurring for type(s) { (2,3,12), (2,4,6) } Genus 93 Maximum order 768 occurring for type(s) { (2,4,96) } Genus 94 Maximum order 2232 occurring for type(s) { (2,3,12) } Genus 95 Maximum order 768 occurring for type(s) { (2,4,192) } Genus 96 Maximum order 3420 occurring for type(s) { (2,3,9) } Genus 97 Maximum order 3840 occurring for type(s) { (2,4,5) } Genus 98 Maximum order 1164 occurring for type(s) { (2,6,6) } Genus 99 Maximum order 2352 occurring for type(s) { (2,3,12) } Genus 100 Maximum order 1320 occurring for type(s) { (2,4,10) } Genus 101 Maximum order 2400 occurring for type(s) { (3,3,4) } Genus 102 Maximum order 1010 occurring for type(s) { (2,5,10) } Genus 103 Maximum order 4896 occurring for type(s) { (2,3,8) } Genus 104 Maximum order 1236 occurring for type(s) { (2,6,6) } Genus 105 Maximum order 2496 occurring for type(s) { (2,3,12) } Genus 106 Maximum order 2016 occurring for type(s) { (2,3,16) } Genus 107 Maximum order 1696 occurring for type(s) { (2,4,8) } Genus 108 Maximum order 888 occurring for type(s) { (2,4,111) } Genus 109 Maximum order 5184 occurring for type(s) { (2,3,8) } Genus 110 Maximum order 1308 occurring for type(s) { (2,6,6) } Genus 111 Maximum order 2640 occurring for type(s) { (2,4,6) } Genus 112 Maximum order 2664 occurring for type(s) { (2,3,12) } Genus 113 Maximum order 2688 occurring for type(s) { (2,3,12), (2,4,6) } Genus 114 Maximum order 936 occurring for type(s) { (2,4,117) } Genus 115 Maximum order 3420 occurring for type(s) { (2,3,10) } Genus 116 Maximum order 936 occurring for type(s) { (2,4,234) } Genus 117 Maximum order 1856 occurring for type(s) { (2,4,8) } Genus 118 Maximum order 9828 occurring for type(s) { (2,3,7) } Genus 119 Maximum order 960 occurring for type(s) { (2,4,240) } Genus 120 Maximum order 1734 occurring for type(s) { (2,3,34) } Genus 121 Maximum order 2880 occurring for type(s) { (2,4,6) } Genus 122 Maximum order 5808 occurring for type(s) { (2,3,8) } Genus 123 Maximum order 2928 occurring for type(s) { (2,3,12) } Genus 124 Maximum order 1080 occurring for type(s) { (2,4,45) } Genus 125 Maximum order 1488 occurring for type(s) { (2,6,6) } Genus 126 Maximum order 1500 occurring for type(s) { (2,2,2,3) } Genus 127 Maximum order 3024 occurring for type(s) { (2,3,12) } Genus 128 Maximum order 1524 occurring for type(s) { (2,6,6) } Genus 129 Maximum order 10752 occurring for type(s) { (2,3,7) } Genus 130 Maximum order 3096 occurring for type(s) { (2,3,12) } Genus 131 Maximum order 2080 occurring for type(s) { (2,4,8) } Genus 132 Maximum order 1310 occurring for type(s) { (2,5,10) } Genus 133 Maximum order 3960 occurring for type(s) { (2,3,10) } Genus 134 Maximum order 1596 occurring for type(s) { (2,6,6) } Genus 135 Maximum order 3216 occurring for type(s) { (2,3,12) } Genus 136 Maximum order 6480 occurring for type(s) { (2,3,8) } Genus 137 Maximum order 2176 occurring for type(s) { (2,4,8) } Genus 138 Maximum order 1128 occurring for type(s) { (2,4,141) } Genus 139 Maximum order 1152 occurring for type(s) { (2,4,96) } Genus 140 Maximum order 1668 occurring for type(s) { (2,6,6) } Genus 141 Maximum order 2184 occurring for type(s) { (2,3,26) } Genus 142 Maximum order 1144 occurring for type(s) { (2,4,286) } Genus 143 Maximum order 1152 occurring for type(s) { (2,4,288) } Genus 144 Maximum order 1352 occurring for type(s) { (2,4,26) } Genus 145 Maximum order 6912 occurring for type(s) { (2,3,8) } Genus 146 Maximum order 12180 occurring for type(s) { (2,3,7) } Genus 147 Maximum order 3504 occurring for type(s) { (2,3,12) } Genus 148 Maximum order 3528 occurring for type(s) { (2,3,12) } Genus 149 Maximum order 2368 occurring for type(s) { (2,4,8) } Genus 150 Maximum order 1224 occurring for type(s) { (2,4,153) } Genus 151 Maximum order 3600 occurring for type(s) { (2,3,12) } Genus 152 Maximum order 1812 occurring for type(s) { (2,6,6) } Genus 153 Maximum order 3648 occurring for type(s) { (2,3,12) } Genus 154 Maximum order 2448 occurring for type(s) { (2,4,8) } Genus 155 Maximum order 1320 occurring for type(s) { (2,6,10) } Genus 156 Maximum order 1550 occurring for type(s) { (2,5,10) } Genus 157 Maximum order 3744 occurring for type(s) { (2,3,12) } Genus 158 Maximum order 1884 occurring for type(s) { (2,6,6) } Genus 159 Maximum order 3792 occurring for type(s) { (2,3,12) } Genus 160 Maximum order 1288 occurring for type(s) { (2,4,322) } Genus 161 Maximum order 3840 occurring for type(s) { (2,4,6) } Genus 162 Maximum order 1320 occurring for type(s) { (2,4,165) } Genus 163 Maximum order 3888 occurring for type(s) { (2,3,12) } Genus 164 Maximum order 1956 occurring for type(s) { (2,6,6) } Genus 165 Maximum order 2624 occurring for type(s) { (2,4,8) } Genus 166 Maximum order 6600 occurring for type(s) { (2,4,5) } Genus 167 Maximum order 1344 occurring for type(s) { (2,4,336) } Genus 168 Maximum order 1368 occurring for type(s) { (2,4,171) } Genus 169 Maximum order 8064 occurring for type(s) { (2,3,8) } Genus 170 Maximum order 4056 occurring for type(s) { (3,3,4), (2,4,6) } Genus 171 Maximum order 2720 occurring for type(s) { (2,4,8) } Genus 172 Maximum order 6840 occurring for type(s) { (2,4,5) } Genus 173 Maximum order 2064 occurring for type(s) { (2,6,6) } Genus 174 Maximum order 1416 occurring for type(s) { (2,4,177) } Genus 175 Maximum order 1856 occurring for type(s) { (2,4,16) } Genus 176 Maximum order 3000 occurring for type(s) { (2,3,20) } Genus 177 Maximum order 2640 occurring for type(s) { (2,5,6) } Genus 178 Maximum order 1432 occurring for type(s) { (2,4,358) } Genus 179 Maximum order 2848 occurring for type(s) { (2,4,8) } Genus 180 Maximum order 1464 occurring for type(s) { (2,4,183) } Genus 181 Maximum order 8640 occurring for type(s) { (2,3,8) } Genus 182 Maximum order 2172 occurring for type(s) { (2,6,6) } Genus 183 Maximum order 4368 occurring for type(s) { (2,3,12), (2,4,6) } Genus 184 Maximum order 4392 occurring for type(s) { (2,3,12) } Genus 185 Maximum order 1600 occurring for type(s) { (2,4,50) } Genus 186 Maximum order 1512 occurring for type(s) { (2,4,189) } Genus 187 Maximum order 4464 occurring for type(s) { (2,3,12) } Genus 188 Maximum order 1512 occurring for type(s) { (2,4,378) } Genus 189 Maximum order 1536 occurring for type(s) { (2,4,192) } Genus 190 Maximum order 4536 occurring for type(s) { (2,3,12) } Genus 191 Maximum order 2640 occurring for type(s) { (2,3,44) } Genus 192 Maximum order 1910 occurring for type(s) { (2,5,10) } Genus 193 Maximum order 5760 occurring for type(s) { (2,3,10) } Genus 194 Maximum order 2316 occurring for type(s) { (2,6,6) } Genus 195 Maximum order 4656 occurring for type(s) { (2,3,12) } Genus 196 Maximum order 3420 occurring for type(s) { (2,3,19) } Genus 197 Maximum order 4704 occurring for type(s) { (3,3,4), (2,4,6) } Genus 198 Maximum order 1608 occurring for type(s) { (2,4,201) } Genus 199 Maximum order 2640 occurring for type(s) { (2,4,10) } Genus 200 Maximum order 2388 occurring for type(s) { (2,6,6) } Genus 201 Maximum order 4800 occurring for type(s) { (2,3,12) } Genus 202 Maximum order 4824 occurring for type(s) { (2,3,12) } Genus 203 Maximum order 3232 occurring for type(s) { (2,4,8) } Genus 204 Maximum order 1656 occurring for type(s) { (2,4,207) } Genus 205 Maximum order 7344 occurring for type(s) { (2,3,9) } Genus 206 Maximum order 2050 occurring for type(s) { (2,5,10) } Genus 207 Maximum order 4944 occurring for type(s) { (2,3,12) } Genus 208 Maximum order 1672 occurring for type(s) { (2,4,418) } Genus 209 Maximum order 4368 occurring for type(s) { (2,3,14) } Genus 210 Maximum order 2904 occurring for type(s) { (2,3,44) } Genus 211 Maximum order 5040 occurring for type(s) { (2,3,12), (2,4,6) } Genus 212 Maximum order 2532 occurring for type(s) { (2,6,6) } Genus 213 Maximum order 3392 occurring for type(s) { (2,4,8) } Genus 214 Maximum order 1720 occurring for type(s) { (2,4,430) } Genus 215 Maximum order 1728 occurring for type(s) { (2,4,432) } Genus 216 Maximum order 1800 occurring for type(s) { (2,4,90) } Genus 217 Maximum order 6480 occurring for type(s) { (2,3,10) } Genus 218 Maximum order 2604 occurring for type(s) { (2,6,6) } Genus 219 Maximum order 5232 occurring for type(s) { (2,3,12) } Genus 220 Maximum order 5256 occurring for type(s) { (2,3,12) } Genus 221 Maximum order 5280 occurring for type(s) { (2,4,6) } Genus 222 Maximum order 1800 occurring for type(s) { (2,4,225) } Genus 223 Maximum order 5328 occurring for type(s) { (2,3,12) } Genus 224 Maximum order 2676 occurring for type(s) { (2,6,6) } Genus 225 Maximum order 5376 occurring for type(s) { (2,3,12) } Genus 226 Maximum order 5400 occurring for type(s) { (2,3,12), (3,3,4) } Genus 227 Maximum order 3616 occurring for type(s) { (2,4,8) } Genus 228 Maximum order 1848 occurring for type(s) { (2,4,231) } Genus 229 Maximum order 6840 occurring for type(s) { (2,3,10) } Genus 230 Maximum order 2748 occurring for type(s) { (2,6,6) } Genus 231 Maximum order 6072 occurring for type(s) { (2,3,11) } Genus 232 Maximum order 3276 occurring for type(s) { (2,3,39) } Genus 233 Maximum order 3712 occurring for type(s) { (2,4,8) } Genus 234 Maximum order 1896 occurring for type(s) { (2,4,237) } Genus 235 Maximum order 11232 occurring for type(s) { (2,3,8) } Genus 236 Maximum order 1896 occurring for type(s) { (2,4,474) } Genus 237 Maximum order 1920 occurring for type(s) { (2,4,240) } Genus 238 Maximum order 5688 occurring for type(s) { (2,3,12) } Genus 239 Maximum order 2176 occurring for type(s) { (2,4,32) } Genus 240 Maximum order 1944 occurring for type(s) { (2,4,243) } Genus 241 Maximum order 9600 occurring for type(s) { (2,4,5) } Genus 242 Maximum order 2892 occurring for type(s) { (2,6,6) } Genus 243 Maximum order 5808 occurring for type(s) { (2,3,12) } Genus 244 Maximum order 11664 occurring for type(s) { (2,3,8) } Genus 245 Maximum order 3904 occurring for type(s) { (2,4,8) } Genus 246 Maximum order 4116 occurring for type(s) { (2,3,21) } Genus 247 Maximum order 2624 occurring for type(s) { (2,4,16) } Genus 248 Maximum order 2964 occurring for type(s) { (2,6,6) } Genus 249 Maximum order 5952 occurring for type(s) { (2,3,12) } Genus 250 Maximum order 2008 occurring for type(s) { (2,4,502) } Genus 251 Maximum order 12000 occurring for type(s) { (2,3,8) } Genus 252 Maximum order 2510 occurring for type(s) { (2,5,10) } Genus 253 Maximum order 6048 occurring for type(s) { (2,3,12) } Genus 254 Maximum order 12144 occurring for type(s) { (2,3,8) } Genus 255 Maximum order 6096 occurring for type(s) { (2,3,12) } Genus 256 Maximum order 4896 occurring for type(s) { (2,3,16) } Genus 257 Maximum order 12288 occurring for type(s) { (2,3,8) } Genus 258 Maximum order 2088 occurring for type(s) { (2,4,261) } Genus 259 Maximum order 6192 occurring for type(s) { (2,3,12) } Genus 260 Maximum order 3108 occurring for type(s) { (2,6,6) } Genus 261 Maximum order 4160 occurring for type(s) { (2,4,8) } Genus 262 Maximum order 3132 occurring for type(s) { (2,4,12) } Genus 263 Maximum order 2112 occurring for type(s) { (2,4,528) } Genus 264 Maximum order 2136 occurring for type(s) { (2,4,267) } Genus 265 Maximum order 7920 occurring for type(s) { (2,3,10) } Genus 266 Maximum order 2200 occurring for type(s) { (2,4,110) } Genus 267 Maximum order 6384 occurring for type(s) { (2,3,12) } Genus 268 Maximum order 2152 occurring for type(s) { (2,4,538) } Genus 269 Maximum order 3216 occurring for type(s) { (2,6,6) } Genus 270 Maximum order 2184 occurring for type(s) { (2,4,273) } Genus 271 Maximum order 5040 occurring for type(s) { (2,4,7) } Genus 272 Maximum order 3252 occurring for type(s) { (2,6,6) } Genus 273 Maximum order 4896 occurring for type(s) { (2,3,18) } Genus 274 Maximum order 6552 occurring for type(s) { (2,3,12), (2,4,6) } Genus 275 Maximum order 4384 occurring for type(s) { (2,4,8) } Genus 276 Maximum order 3750 occurring for type(s) { (2,3,50) } Genus 277 Maximum order 2304 occurring for type(s) { (2,4,96) } Genus 278 Maximum order 3324 occurring for type(s) { (2,6,6) } Genus 279 Maximum order 6672 occurring for type(s) { (2,3,12) } Genus 280 Maximum order 6696 occurring for type(s) { (2,3,12) } Genus 281 Maximum order 2688 occurring for type(s) { (2,4,24), (3,3,8), (2,6,8) } Genus 282 Maximum order 2810 occurring for type(s) { (2,5,10) } Genus 283 Maximum order 2304 occurring for type(s) { (2,4,192) } Genus 284 Maximum order 3396 occurring for type(s) { (2,6,6) } Genus 285 Maximum order 2400 occurring for type(s) { (2,4,75) } Genus 286 Maximum order 10260 occurring for type(s) { (2,3,9) } Genus 287 Maximum order 4368 occurring for type(s) { (2,3,28) } Genus 288 Maximum order 2328 occurring for type(s) { (2,4,291) } Genus 289 Maximum order 13824 occurring for type(s) { (2,3,8) } Genus 290 Maximum order 13872 occurring for type(s) { (2,3,8) } Genus 291 Maximum order 4640 occurring for type(s) { (2,4,8) } Genus 292 Maximum order 6984 occurring for type(s) { (2,3,12) } Genus 293 Maximum order 4672 occurring for type(s) { (2,4,8) } Genus 294 Maximum order 2376 occurring for type(s) { (2,4,297) } Genus 295 Maximum order 7056 occurring for type(s) { (2,3,12) } Genus 296 Maximum order 2376 occurring for type(s) { (2,4,594) } Genus 297 Maximum order 7104 occurring for type(s) { (2,3,12) } Genus 298 Maximum order 3888 occurring for type(s) { (2,3,72) } Genus 299 Maximum order 4768 occurring for type(s) { (2,4,8) } Genus 300 Maximum order 4056 occurring for type(s) { (2,3,52) } Genus 301 Maximum order 9000 occurring for type(s) { (2,3,10) } ........................................................................... Case B: All automorphisms [with * indicating that orientation-reversing automorphisms occur] Genus 2 Maximum order 96 occurring for type(s) { (2,3,8)* } Genus 3 Maximum order 336 occurring for type(s) { (2,3,7)* } Genus 4 Maximum order 240 occurring for type(s) { (2,4,5)* } Genus 5 Maximum order 384 occurring for type(s) { (2,3,8)* } Genus 6 Maximum order 300 occurring for type(s) { (2,3,10)* } Genus 7 Maximum order 1008 occurring for type(s) { (2,3,7)* } Genus 8 Maximum order 672 occurring for type(s) { (2,3,8)* } Genus 9 Maximum order 640 occurring for type(s) { (2,4,5)* } Genus 10 Maximum order 720 occurring for type(s) { (2,4,5)* } Genus 11 Maximum order 480 occurring for type(s) { (2,4,6)* } Genus 12 Maximum order 240 occurring for type(s) { (2,4,15)* } Genus 13 Maximum order 720 occurring for type(s) { (2,3,10)* } Genus 14 Maximum order 2184 occurring for type(s) { (2,3,7)* } Genus 15 Maximum order 1008 occurring for type(s) { (2,3,9)* } Genus 16 Maximum order 1440 occurring for type(s) { (2,3,8)* } Genus 17 Maximum order 1536 occurring for type(s) { (2,3,8)* } Genus 18 Maximum order 336 occurring for type(s) { (2,4,21)* } Genus 19 Maximum order 1440 occurring for type(s) { (2,4,5)* } Genus 20 Maximum order 336 occurring for type(s) { (2,4,42)* } Genus 21 Maximum order 960 occurring for type(s) { (2,4,6)* } Genus 22 Maximum order 2016 occurring for type(s) { (2,3,8)* } Genus 23 Maximum order 384 occurring for type(s) { (2,4,48)* } Genus 24 Maximum order 432 occurring for type(s) { (2,4,27)* } Genus 25 Maximum order 1440 occurring for type(s) { (2,3,10)* } Genus 26 Maximum order 1500 occurring for type(s) { (2,3,10)* } Genus 27 Maximum order 624 occurring for type(s) { (2,3,12) } Genus 28 Maximum order 1296 occurring for type(s) { (2,3,12)*, (2,3,8), (2,4,6)* } Genus 29 Maximum order 1344 occurring for type(s) { (2,4,6)* } Genus 30 Maximum order 528 occurring for type(s) { (2,4,33)* } Genus 31 Maximum order 1440 occurring for type(s) { (2,4,6)* } Genus 32 Maximum order 528 occurring for type(s) { (2,4,66)* } Genus 33 Maximum order 3072 occurring for type(s) { (2,3,8)* } Genus 34 Maximum order 2640 occurring for type(s) { (2,4,5)* } Genus 35 Maximum order 576 occurring for type(s) { (2,4,72)* } Genus 36 Maximum order 1344 occurring for type(s) { (2,3,16)* } Genus 37 Maximum order 1728 occurring for type(s) { (3,3,4)*, (2,3,12)*, (2,3,8), (2,4,6)* } Genus 38 Maximum order 624 occurring for type(s) { (2,4,78)* } Genus 39 Maximum order 912 occurring for type(s) { (2,3,12) } Genus 40 Maximum order 936 occurring for type(s) { (2,3,12) } Genus 41 Maximum order 1920 occurring for type(s) { (2,4,6)* } Genus 42 Maximum order 720 occurring for type(s) { (2,4,45)* } Genus 43 Maximum order 3024 occurring for type(s) { (2,3,9)* } Genus 44 Maximum order 720 occurring for type(s) { (2,4,90)* } Genus 45 Maximum order 2640 occurring for type(s) { (2,3,10)* } Genus 46 Maximum order 4320 occurring for type(s) { (2,3,8)* } Genus 47 Maximum order 768 occurring for type(s) { (2,4,96)* } Genus 48 Maximum order 816 occurring for type(s) { (2,4,51)* } Genus 49 Maximum order 3840 occurring for type(s) { (2,4,5)* } Genus 50 Maximum order 2184 occurring for type(s) { (2,3,13)* } Genus 51 Maximum order 2400 occurring for type(s) { (2,3,12)* } Genus 52 Maximum order 4896 occurring for type(s) { (2,3,8)* } Genus 53 Maximum order 960 occurring for type(s) { (2,4,30)* } Genus 54 Maximum order 912 occurring for type(s) { (2,4,57)* } Genus 55 Maximum order 2592 occurring for type(s) { (2,3,12)*, (2,4,6)* } Genus 56 Maximum order 2640 occurring for type(s) { (2,3,12)*, (2,4,6)* } Genus 57 Maximum order 2688 occurring for type(s) { (2,4,6)* } Genus 58 Maximum order 1368 occurring for type(s) { (2,3,12) } Genus 59 Maximum order 960 occurring for type(s) { (2,4,120)* } Genus 60 Maximum order 1008 occurring for type(s) { (2,4,63)* } Genus 61 Maximum order 2880 occurring for type(s) { (2,4,6)* } Genus 62 Maximum order 1008 occurring for type(s) { (2,4,126)* } Genus 63 Maximum order 1488 occurring for type(s) { (2,3,12) } Genus 64 Maximum order 2016 occurring for type(s) { (2,3,24)* } Genus 65 Maximum order 6144 occurring for type(s) { (2,3,8)* } Genus 66 Maximum order 2028 occurring for type(s) { (2,3,26)* } Genus 67 Maximum order 1152 occurring for type(s) { (2,4,48)* } Genus 68 Maximum order 1104 occurring for type(s) { (2,4,138)* } Genus 69 Maximum order 4896 occurring for type(s) { (2,3,9)* } Genus 70 Maximum order 1320 occurring for type(s) { (2,5,11)* } Genus 71 Maximum order 1344 occurring for type(s) { (2,6,8)* } Genus 72 Maximum order 1200 occurring for type(s) { (2,4,75)* } Genus 73 Maximum order 4320 occurring for type(s) { (2,3,10)* } Genus 74 Maximum order 1200 occurring for type(s) { (2,4,150)* } Genus 75 Maximum order 1776 occurring for type(s) { (2,3,12) } Genus 76 Maximum order 3600 occurring for type(s) { (2,3,12)* } Genus 77 Maximum order 1344 occurring for type(s) { (2,4,42)* } Genus 78 Maximum order 2352 occurring for type(s) { (2,3,28)* } Genus 79 Maximum order 1872 occurring for type(s) { (2,3,12) } Genus 80 Maximum order 1296 occurring for type(s) { (2,4,162)* } Genus 81 Maximum order 3072 occurring for type(s) { (2,3,16)* } Genus 82 Maximum order 7776 occurring for type(s) { (2,3,8)* } Genus 83 Maximum order 1344 occurring for type(s) { (2,4,168)* } Genus 84 Maximum order 1392 occurring for type(s) { (2,4,87)* } Genus 85 Maximum order 8064 occurring for type(s) { (2,3,8)* } Genus 86 Maximum order 2400 occurring for type(s) { (2,3,40)* } Genus 87 Maximum order 2064 occurring for type(s) { (2,3,12) } Genus 88 Maximum order 1424 occurring for type(s) { (2,4,178)* } Genus 89 Maximum order 5280 occurring for type(s) { (2,3,10)* } Genus 90 Maximum order 1488 occurring for type(s) { (2,4,93)* } Genus 91 Maximum order 7200 occurring for type(s) { (2,4,5)* } Genus 92 Maximum order 4368 occurring for type(s) { (2,3,12)*, (2,4,6)* } Genus 93 Maximum order 1536 occurring for type(s) { (2,4,96)* } Genus 94 Maximum order 2232 occurring for type(s) { (2,3,12) } Genus 95 Maximum order 1536 occurring for type(s) { (2,4,192)* } Genus 96 Maximum order 6840 occurring for type(s) { (2,3,9)* } Genus 97 Maximum order 7680 occurring for type(s) { (2,4,5)* } Genus 98 Maximum order 1584 occurring for type(s) { (2,4,198)* } Genus 99 Maximum order 4704 occurring for type(s) { (2,3,12)* } Genus 100 Maximum order 2640 occurring for type(s) { (2,4,10)* } Genus 101 Maximum order 4800 occurring for signature (0; +; [3]; {(4)}) Genus 102 Maximum order 1680 occurring for type(s) { (2,4,105)* } Genus 103 Maximum order 9792 occurring for type(s) { (2,3,8)* } Genus 104 Maximum order 1680 occurring for type(s) { (2,4,210)* } Genus 105 Maximum order 4368 occurring for type(s) { (2,3,14)* } Genus 106 Maximum order 4032 occurring for type(s) { (2,3,16)* } Genus 107 Maximum order 1728 occurring for type(s) { (2,4,216)* } Genus 108 Maximum order 1776 occurring for type(s) { (2,4,111)* } Genus 109 Maximum order 5184 occurring for type(s) { (2,3,12)*, (2,3,8), (2,4,6)* } Genus 110 Maximum order 1776 occurring for type(s) { (2,4,222)* } Genus 111 Maximum order 5280 occurring for type(s) { (2,4,6)* } Genus 112 Maximum order 2664 occurring for type(s) { (2,3,12) } Genus 113 Maximum order 5376 occurring for type(s) { (2,4,6)* } Genus 114 Maximum order 1872 occurring for type(s) { (2,4,117)* } Genus 115 Maximum order 6840 occurring for type(s) { (2,3,10)* } Genus 116 Maximum order 1872 occurring for type(s) { (2,4,234)* } Genus 117 Maximum order 1920 occurring for type(s) { (2,4,120)* } Genus 118 Maximum order 19656 occurring for type(s) { (2,3,7)* } Genus 119 Maximum order 1920 occurring for type(s) { (2,4,240)* } Genus 120 Maximum order 3468 occurring for type(s) { (2,3,34)* } Genus 121 Maximum order 5760 occurring for type(s) { (2,4,6)* } Genus 122 Maximum order 5808 occurring for type(s) { (3,3,4)*, (2,3,8) } Genus 123 Maximum order 2928 occurring for type(s) { (2,3,12) } Genus 124 Maximum order 2160 occurring for type(s) { (2,4,45)* } Genus 125 Maximum order 2240 occurring for type(s) { (2,4,35)* } Genus 126 Maximum order 3000 occurring for type(s) { (2,2,2,3)* } Genus 127 Maximum order 4704 occurring for type(s) { (2,4,7)* } Genus 128 Maximum order 2064 occurring for type(s) { (2,4,258)* } Genus 129 Maximum order 21504 occurring for type(s) { (2,3,7)* } Genus 130 Maximum order 3096 occurring for type(s) { (2,3,12) } Genus 131 Maximum order 2400 occurring for type(s) { (2,5,12)*, (2,4,30)* } Genus 132 Maximum order 2160 occurring for type(s) { (2,4,135)* } Genus 133 Maximum order 7920 occurring for type(s) { (2,3,10)* } Genus 134 Maximum order 2352 occurring for type(s) { (2,4,42)* } Genus 135 Maximum order 3216 occurring for type(s) { (2,3,12) } Genus 136 Maximum order 12960 occurring for type(s) { (2,3,8)* } Genus 137 Maximum order 2304 occurring for type(s) { (2,4,72)* } Genus 138 Maximum order 2256 occurring for type(s) { (2,4,141)* } Genus 139 Maximum order 2304 occurring for type(s) { (2,4,96)* } Genus 140 Maximum order 2256 occurring for type(s) { (2,4,282)* } Genus 141 Maximum order 4368 occurring for type(s) { (2,3,26)* } Genus 142 Maximum order 2288 occurring for type(s) { (2,4,286)* } Genus 143 Maximum order 2304 occurring for type(s) { (2,4,288)* } Genus 144 Maximum order 2704 occurring for type(s) { (2,4,26)* } Genus 145 Maximum order 8640 occurring for type(s) { (2,3,10)* } Genus 146 Maximum order 24360 occurring for type(s) { (2,3,7)* } Genus 147 Maximum order 3504 occurring for type(s) { (2,3,12) } Genus 148 Maximum order 7056 occurring for type(s) { (2,3,12)* } Genus 149 Maximum order 2496 occurring for type(s) { (2,4,78)* } Genus 150 Maximum order 2448 occurring for type(s) { (2,4,153)* } Genus 151 Maximum order 7200 occurring for type(s) { (2,3,12)* } Genus 152 Maximum order 2448 occurring for type(s) { (2,4,306)* } Genus 153 Maximum order 4332 occurring for type(s) { (2,3,38)* } Genus 154 Maximum order 4896 occurring for type(s) { (2,4,8)* } Genus 155 Maximum order 2640 occurring for type(s) { (2,6,10)* } Genus 156 Maximum order 2544 occurring for type(s) { (2,4,159)* } Genus 157 Maximum order 4032 occurring for type(s) { (2,3,84)* } Genus 158 Maximum order 2544 occurring for type(s) { (2,4,318)* } Genus 159 Maximum order 3792 occurring for type(s) { (2,3,12) } Genus 160 Maximum order 2576 occurring for type(s) { (2,4,322)* } Genus 161 Maximum order 7680 occurring for type(s) { (2,4,6)* } Genus 162 Maximum order 2640 occurring for type(s) { (2,4,165)* } Genus 163 Maximum order 7776 occurring for type(s) { (2,3,12)* } Genus 164 Maximum order 2640 occurring for type(s) { (2,4,330)* } Genus 165 Maximum order 2880 occurring for type(s) { (2,4,45)* } Genus 166 Maximum order 13200 occurring for type(s) { (2,4,5)* } Genus 167 Maximum order 2688 occurring for type(s) { (2,4,336)* } Genus 168 Maximum order 2736 occurring for type(s) { (2,4,171)* } Genus 169 Maximum order 16128 occurring for type(s) { (2,3,8)* } Genus 170 Maximum order 8112 occurring for signature (0; +; [3]; {(4)}) Genus 171 Maximum order 4896 occurring for type(s) { (2,4,9)* } Genus 172 Maximum order 13680 occurring for type(s) { (2,4,5)* } Genus 173 Maximum order 2880 occurring for type(s) { (2,4,90)* } Genus 174 Maximum order 2832 occurring for type(s) { (2,4,177)* } Genus 175 Maximum order 2880 occurring for type(s) { (2,4,120)* } Genus 176 Maximum order 6000 occurring for type(s) { (2,3,20)* } Genus 177 Maximum order 5280 occurring for type(s) { (2,5,6)* } Genus 178 Maximum order 2864 occurring for type(s) { (2,4,358)* } Genus 179 Maximum order 2880 occurring for type(s) { (2,4,360)* } Genus 180 Maximum order 2928 occurring for type(s) { (2,4,183)* } Genus 181 Maximum order 17280 occurring for type(s) { (2,3,8)* } Genus 182 Maximum order 2928 occurring for type(s) { (2,4,366)* } Genus 183 Maximum order 8736 occurring for type(s) { (2,4,6)* } Genus 184 Maximum order 4392 occurring for type(s) { (2,3,12) } Genus 185 Maximum order 3200 occurring for type(s) { (2,4,50)* } Genus 186 Maximum order 3024 occurring for type(s) { (2,4,189)* } Genus 187 Maximum order 4464 occurring for type(s) { (2,3,12) } Genus 188 Maximum order 3024 occurring for type(s) { (2,4,378)* } Genus 189 Maximum order 3072 occurring for type(s) { (2,4,192)* } Genus 190 Maximum order 6048 occurring for type(s) { (2,3,24)* } Genus 191 Maximum order 5280 occurring for type(s) { (2,3,44)* } Genus 192 Maximum order 3120 occurring for type(s) { (2,4,195)* } Genus 193 Maximum order 11520 occurring for type(s) { (2,3,10)* } Genus 194 Maximum order 3120 occurring for type(s) { (2,4,390)* } Genus 195 Maximum order 4656 occurring for type(s) { (2,3,12) } Genus 196 Maximum order 6840 occurring for type(s) { (2,3,19)* } Genus 197 Maximum order 6272 occurring for type(s) { (2,4,8)* } Genus 198 Maximum order 3216 occurring for type(s) { (2,4,201)* } Genus 199 Maximum order 5280 occurring for type(s) { (2,4,10)* } Genus 200 Maximum order 3216 occurring for type(s) { (2,4,402)* } Genus 201 Maximum order 9600 occurring for type(s) { (2,3,12)* } Genus 202 Maximum order 4824 occurring for type(s) { (2,3,12) } Genus 203 Maximum order 3264 occurring for type(s) { (2,4,408)* } Genus 204 Maximum order 3312 occurring for type(s) { (2,4,207)* } Genus 205 Maximum order 14688 occurring for type(s) { (2,3,9)* } Genus 206 Maximum order 3312 occurring for type(s) { (2,4,414)* } Genus 207 Maximum order 4944 occurring for type(s) { (2,3,12) } Genus 208 Maximum order 3344 occurring for type(s) { (2,4,418)* } Genus 209 Maximum order 8736 occurring for type(s) { (2,3,14)* } Genus 210 Maximum order 5808 occurring for type(s) { (2,3,44)* } Genus 211 Maximum order 10080 occurring for type(s) { (2,3,12)* } Genus 212 Maximum order 3408 occurring for type(s) { (2,4,426)* } Genus 213 Maximum order 3456 occurring for type(s) { (2,4,216)* } Genus 214 Maximum order 3440 occurring for type(s) { (2,4,430)* } Genus 215 Maximum order 3456 occurring for type(s) { (2,4,432)* } Genus 216 Maximum order 3600 occurring for type(s) { (2,4,90)* } Genus 217 Maximum order 12960 occurring for type(s) { (2,3,10)* } Genus 218 Maximum order 3504 occurring for type(s) { (2,4,438)* } Genus 219 Maximum order 5232 occurring for type(s) { (2,3,12) } Genus 220 Maximum order 5256 occurring for type(s) { (2,3,12) } Genus 221 Maximum order 10560 occurring for type(s) { (2,4,6)* } Genus 222 Maximum order 3600 occurring for type(s) { (2,4,225)* } Genus 223 Maximum order 5328 occurring for type(s) { (2,3,12) } Genus 224 Maximum order 3600 occurring for type(s) { (2,4,450)* } Genus 225 Maximum order 7680 occurring for type(s) { (2,3,20)* } Genus 226 Maximum order 10800 occurring for type(s) { (2,3,12)* } Genus 227 Maximum order 3648 occurring for type(s) { (2,4,456)* } Genus 228 Maximum order 3696 occurring for type(s) { (2,4,231)* } Genus 229 Maximum order 13680 occurring for type(s) { (2,3,10)* } Genus 230 Maximum order 3696 occurring for type(s) { (2,4,462)* } Genus 231 Maximum order 12144 occurring for type(s) { (2,3,11)* } Genus 232 Maximum order 6552 occurring for type(s) { (2,3,39)* } Genus 233 Maximum order 3840 occurring for type(s) { (2,4,120)* } Genus 234 Maximum order 3792 occurring for type(s) { (2,4,237)* } Genus 235 Maximum order 22464 occurring for type(s) { (2,3,8)* } Genus 236 Maximum order 3792 occurring for type(s) { (2,4,474)* } Genus 237 Maximum order 3840 occurring for type(s) { (2,4,240)* } Genus 238 Maximum order 5688 occurring for type(s) { (2,3,12) } Genus 239 Maximum order 3840 occurring for type(s) { (2,4,480)* } Genus 240 Maximum order 3888 occurring for type(s) { (2,4,243)* } Genus 241 Maximum order 19200 occurring for type(s) { (2,4,5)* } Genus 242 Maximum order 3888 occurring for type(s) { (2,4,486)* } Genus 243 Maximum order 11616 occurring for type(s) { (2,3,12)* } Genus 244 Maximum order 23328 occurring for type(s) { (2,3,8)* } Genus 245 Maximum order 4160 occurring for type(s) { (2,4,65)* } Genus 246 Maximum order 8232 occurring for type(s) { (2,3,21)* } Genus 247 Maximum order 4032 occurring for type(s) { (2,4,168)* } Genus 248 Maximum order 3984 occurring for type(s) { (2,4,498)* } Genus 249 Maximum order 5952 occurring for type(s) { (2,3,12) } Genus 250 Maximum order 4016 occurring for type(s) { (2,4,502)* } Genus 251 Maximum order 12000 occurring for type(s) { (2,3,8), (2,4,6)* } Genus 252 Maximum order 4080 occurring for type(s) { (2,4,255)* } Genus 253 Maximum order 11232 occurring for type(s) { (2,3,13)* } Genus 254 Maximum order 24288 occurring for type(s) { (2,3,8)* } Genus 255 Maximum order 6096 occurring for type(s) { (2,3,12) } Genus 256 Maximum order 9792 occurring for type(s) { (2,3,16)* } Genus 257 Maximum order 24576 occurring for type(s) { (2,3,8)* } Genus 258 Maximum order 4176 occurring for type(s) { (2,4,261)* } Genus 259 Maximum order 6192 occurring for type(s) { (2,3,12) } Genus 260 Maximum order 4176 occurring for type(s) { (2,4,522)* } Genus 261 Maximum order 4800 occurring for type(s) { (2,4,30)* } Genus 262 Maximum order 4208 occurring for type(s) { (2,4,526)* } Genus 263 Maximum order 4224 occurring for type(s) { (2,4,528)* } Genus 264 Maximum order 4272 occurring for type(s) { (2,4,267)* } Genus 265 Maximum order 15840 occurring for type(s) { (2,3,10)* } Genus 266 Maximum order 4400 occurring for type(s) { (2,4,110)* } Genus 267 Maximum order 6384 occurring for type(s) { (2,3,12) } Genus 268 Maximum order 4304 occurring for type(s) { (2,4,538)* } Genus 269 Maximum order 4416 occurring for type(s) { (2,4,138)* } Genus 270 Maximum order 4368 occurring for type(s) { (2,4,273)* } Genus 271 Maximum order 10080 occurring for type(s) { (2,4,7)* } Genus 272 Maximum order 4368 occurring for type(s) { (2,4,546)* } Genus 273 Maximum order 9792 occurring for type(s) { (2,3,18)* } Genus 274 Maximum order 13104 occurring for type(s) { (2,3,12)*, (2,4,6)* } Genus 275 Maximum order 4416 occurring for type(s) { (2,4,552)* } Genus 276 Maximum order 7500 occurring for type(s) { (2,3,50)* } Genus 277 Maximum order 4608 occurring for type(s) { (2,4,96)* } Genus 278 Maximum order 4464 occurring for type(s) { (2,4,558)* } Genus 279 Maximum order 6672 occurring for type(s) { (2,3,12) } Genus 280 Maximum order 6696 occurring for type(s) { (2,3,12) } Genus 281 Maximum order 5376 occurring for type(s) { (2,6,8)*, (2,4,24)*, (3,3,8)* } and signature (0; +; [3]; {(8)}) Genus 282 Maximum order 4560 occurring for type(s) { (2,4,285)* } Genus 283 Maximum order 4608 occurring for type(s) { (2,4,192)* } Genus 284 Maximum order 4560 occurring for type(s) { (2,4,570)* } Genus 285 Maximum order 4800 occurring for type(s) { (2,4,75)* } Genus 286 Maximum order 20520 occurring for type(s) { (2,3,9)* } Genus 287 Maximum order 8736 occurring for type(s) { (2,3,28)* } Genus 288 Maximum order 4656 occurring for type(s) { (2,4,291)* } Genus 289 Maximum order 13824 occurring for type(s) { (3,3,4)*, (2,3,12)*, (2,3,8), (2,4,6)* } Genus 290 Maximum order 13872 occurring for type(s) { (3,3,4)*, (2,3,8) } and signature (0; +; [3]; {(4)}) Genus 291 Maximum order 4800 occurring for type(s) { (2,4,120)* } Genus 292 Maximum order 6984 occurring for type(s) { (2,3,12) } Genus 293 Maximum order 4800 occurring for type(s) { (2,4,150)* } Genus 294 Maximum order 4752 occurring for type(s) { (2,4,297)* } Genus 295 Maximum order 14112 occurring for type(s) { (2,3,12)* } Genus 296 Maximum order 4752 occurring for type(s) { (2,4,594)* } Genus 297 Maximum order 7104 occurring for type(s) { (2,3,12) } Genus 298 Maximum order 7776 occurring for type(s) { (2,3,72)* } Genus 299 Maximum order 4800 occurring for type(s) { (2,4,600)* } Genus 300 Maximum order 8112 occurring for type(s) { (2,3,52)* } Genus 301 Maximum order 18000 occurring for type(s) { (2,3,10)* } ...........................................................................